A Problem Text in Advanced Calculus by John M. Erdman - Free PDF
A Problem Text in Advanced Calculus - Table of Contents
Intervals - Topology of the Real Line - Continuous Functions from R to R - Sequences of Real Numbers - Connectedness and the Intermediate Value Theorem - Compactness and the Extreme Value Theorem - Limits of Real valued Functions - Differentiation of Real Valued Functions - Matric Spaces - Interiors, Closures and Boundaries - The Topology of Metric Spaces - Sequences in Matric Spaces - Uniform Convergence - More on Continuity and Limits - Compact Metric Spaces - Sequential Characterization of Compactness - Connectedness - Complete Spaces - Applications of a Fixed Point Theorem - Vector Spaces - Linearity - Norms - Continuity and Linearity - The Cauchy Integral - Differential Calculus - Partial Derivatives and Iterated Integrals - Computations - Infinite Series - The Implicit Function Theorem
What You Will Learn in A Problem Text in Advanced Calculus
A Problem Text in Advanced Calculus by John M. Erdman is a unique and rigorous approach to learning upper-level "advanced calculus". Rather than following a traditional lecture-textbook format, this book presents the core material through challenging, well-structured "problem sets" that guide students toward a deeper understanding of the theory behind calculus.
Ideal for math majors or students in physical sciences, the book emphasizes "mathematical proofs", logic, and foundational concepts over computation. Students are encouraged to discover key theorems and results through guided problem-solving, developing the ability to think critically and construct proofs independently. Erdman’s approach is well-suited for inquiry-based learning environments and is often used in “Moore method” or flipped classrooms.
With helpful appendices covering logic, set theory, and proof techniques, this text also serves as a solid transition to "real analysis". It’s a perfect resource for those who want to understand not just how calculus works, but why. Whether used in class or for independent study, Erdman’s problem-focused style makes this book a powerful tool for mastering advanced mathematical thinking.
Book Details & Specifications
Title:
A Problem Text in Advanced Calculus by John M. Erdman - Free PDF
Publisher:
Portland State University
Year:
2008
Pages:
377
Type:
PDF
Language:
English
ISBN-10 #:
1470442469
ISBN-13 #:
978-1470442460
License:
CC
Amazon:
Amazon
About the Author: John M. Erdman
The author
John M. Erdman
is a respected mathematics educator and author, best known for his innovative approach to teaching "advanced calculus". He has taught at Portland State University and specializes in helping students develop strong conceptual understanding through "problem-based learning". His book "A Problem Text in Advanced Calculus" reflects his commitment to "inquiry-based learning", where students explore key mathematical ideas by working through carefully designed problem sets. Erdman’s focus on proofs and logic makes his work a valuable resource for students transitioning to higher-level mathematics.
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